Answer:
B. r=C/2pi
Step-by-step explanation:
C=2piR
C/2pi=R
Surface area of cube = 6 * (side)^2
side^2 = surface area / 6
side = sqrt (surface area / 6)
For the cube with area 1200 square inches:
side = sqrt(surface area / 6)
side = sqrt(1200 / 6)
side = 14.1421 inches
For the cube with area 768 square inches:
side = sqrt(surface area / 6)
side = sqrt(768 / 6)
side = 11.3137 inches
difference between the two lengths = 14.1421 - 11.3137 = 2.8284 inches
Based on the above calculations, the side of the cube with surface area 1200 square inches is 2.8284 inches longer than the side of the cube with surface area 768 square inches
Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}
iren [92.7K]
Answer:
A) a_n = 5n + 2
B) a_n = (2^(n + 1)) - 1
Step-by-step explanation:
A) The sequence is given as;
{7,12,17,22,27,...}
The differences are:
5,5,5,5.
This is an arithmetic sequence following the formula;
a_n = a_1 + (n - 1)d
d is 5
Thus;
a_n = a_1 + (n - 1)5
Now, a_1 = 7. Thus;
a_n = 7 + 5n - 5
a_n = 5n + 2
B) The sequence is given as;
{ 3,7,15,31,63,...}
Now, let's write out the differences of this sequence:
Differences are:
4, 8, 16, 32
This shows that it is a geometric sequence with a common ratio of 2.
In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15
Thus, a_2 = 2a_1 + 1
Also, a_(2 + 1) = 2a_2 + 1
Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1
Thus; a_n can be expressed as:
a_n = (2^(n + 1)) - 1
Answer:
B. 
.
Step-by-step explanation:
Use the power of a power property.
Multiply all the exponents in the parenthesis by 2.
The answer is B. .
Hope this helps!
Answer:
X > -1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
